Finite Group Databasebeta

← #15839220

Subgroups — #15839220

Order 3328.

918 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125216C211yesmaximal, characteristic
2#13124966C212yesmaximal
3#13114057C218yesmaximal, complemented
4#13113562C211yesmaximal, characteristic
5#13113283C212yesmaximal
6C2×Q82×C13C211yesmaximal, characteristic
7Q82×C13—22no—
8Q82×C13—24no—
9Q82×C13C2214yes—
10C2×C13×C4⋊Q8—22no—
11C2×C13×C4⋊Q8—22no—
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C13—22no—
14C2×C4×Q8×C13C2212yes—
15#11719175C2211yescharacteristic
16#11718889—22no—
17#11718886—22no—
18#11718743—22no—
19#11718742C2214yes—
20#11718692C2214yes—
21#11718691—24no—
22#11718681C2214yes—
23#11718632—22no—
24#11718587C2212yes—
25C4×#6099C2211yescharacteristic
26#11718138C2214yes—
27Q8⋊#1055C2218yes—
28C22×Q8×C13—22no—
29C22×Q8×C13D412yes—
30C22×Q8×C13D412yes—
31C13×C4⋊Q8—28no—
32C13×C4⋊Q8—28no—
33C13×C4⋊Q8—28no—
34C13×C4⋊Q8—28no—
35C13×C4⋊Q8—22no—
36C13×C4⋊Q8D412yes—
37C13×C4⋊Q8C2312yes—
38C4×Q8×C13—28no—
39C4×Q8×C13—28no—
40C4×Q8×C13—22no—
41C4×Q8×C13—22no—
42C4×Q8×C13D414yes—
43C4×Q8×C13C2314yes—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C4⋊C4D412yes—
48C2×C42×C13—22no—
49C2×C42×C13—22no—
50C2×C42×C13C2311yescharacteristic
51C2×#6107—24no—
52#88180—21no—
53#88178—22no—
54C2×#6099—21no—
55#88124—21no—
56#88123C2312yes—
57C4×Dic26—22no—
58#88075—24no—
59#88075—28no—
60C22⋊#1055—22no—
61#88050—24no—
62#88048—24no—
63C4⋊#1055C2314yes—
64#88043—22no—
65#88043—21no—
66C4×#1055C2312yes—
67#18551—131nomaximal, Sylow
68C2×Q8×C13—28no—
69C2×Q8×C13—28no—
70C2×Q8×C13—22no—
71C2×Q8×C13—22no—
72C2×Q8×C13—44no—
73C2×Q8×C13—84no—
74C2×Q8×C13C2×D414yes—
75C2×Q8×C13C2×D414yes—
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13C2×D412yes—
80C22×C4×C13C2×D411yescharacteristic
81C2×Dic26—22no—
82C13×C4⋊C4—216no—
83C13×C4⋊C4—24no—
84C13×C4⋊C4—24no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4C2×D414yes—
89C42×C13—28no—
90C42×C13—24no—
91C42×C13—24no—
92C42×C13C2×D412yes—
93C42×C13C2×D411yescharacteristic
94C42×C13C2411yescharacteristic
95C22⋊Dic13—41no—
96#6107—48no—
97C4⋊Dic13—22no—
98C4⋊Dic13—22no—
99#6101—42no—
100C4×Dic13—41no—
101#6099—42no—
102C2×#1055—24no—
103C2×#1055—22no—
104C2×Q82D1311yescharacteristic
105#3139—131no—
106#3113—132no—
107#1645—138no—
108#1558—131no—
109#1491—132no—
110C23×C13#12011yescharacteristic
111Q8×C13—28no—
112Q8×C13—24no—
113Q8×C13—44no—
114Q8×C13—82no—
115Q8×C13—88no—
116Q8×C13#13718yes—
117C2×C4×C13—28no—
118C2×C4×C13—24no—
119C2×C4×C13—22no—
120C2×C4×C13—24no—
121C2×C4×C13—24no—
122C2×C4×C13—24no—
123C2×C4×C13—44no—
124C2×C4×C13—44no—
125C2×C4×C13#12011yescharacteristic
126C2×C4×C13#12012yes—
127C2×C4×C13C22×D411yescharacteristic
128C2×C4×C13C22×D412yes—
129C2×Dic13—42no—
130Dic26—44no—
131#1055—42no—
132#1055—44no—
133Q82—22no—
134Q82—24no—
135Q82C2×D1314yes—
136#533—131no—
137C2×C4⋊Q8—22no—
138C2×C4⋊Q8—22no—
139C2×C4⋊Q8C2×D1311yescharacteristic
140C2×C4×Q8—22no—
141C2×C4×Q8C2×D1312yes—
142#491—262no—
143#487—134no—
144#483—262no—
145#475—134no—
146#462—134no—
147#451—262no—
148#441—264no—
149#432—132no—
150#419—262no—
151C4×M16—131no—
152#333—134no—
153Q8⋊C8—138no—
154C22×C13—22no—
155C22×C13#45512yes—
156C22×C13C2×#12011yescharacteristic
157C4×C13—28no—
158C4×C13—22no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—44no—
162C4×C13—44no—
163C4×C13C2×#13714yes—
164Dic13—82no—
165C22×Q8—22no—
166C22×Q8C22⋊D1312yes—
167C22×Q8C22⋊D1312yes—
168C2×Q16—264no—
169C2×M16—261no—
170C4⋊Q8—28no—
171C4⋊Q8—28no—
172C4⋊Q8—28no—
173C4⋊Q8—28no—
174C4⋊Q8—22no—
175C4⋊Q8—132no—
176C4⋊Q8C22⋊D1312yes—
177C4⋊Q8C22×D1312yes—
178#125—261no—
179C22⋊Q8—262no—
180C4×Q8—28no—
181C4×Q8—28no—
182C4×Q8—22no—
183C4×Q8—22no—
184C4×Q8—262no—
185C4×Q8C22⋊D1314yes—
186C4×Q8C22×D1314yes—
187#117—261no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4C22⋊D1312yes—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42C22×D1311yescharacteristic
195#106—264no—
196C4⋊C8—134no—
197#103—268no—
198#103—264no—
199#103—264no—
200C22⋊C8—262no—
201#97—261no—
202#97—262no—
203C4×C8—132no—
204C2×C13—22no—
205C2×C13#300412yes—
206C2×C13C2×#45511yescharacteristic
207C2×Q8—28no—
208C2×Q8—28no—
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—44no—
212C2×Q8—84no—
213C2×Q8—262no—
214C2×Q8C2×C22⋊D1314yes—
215C2×Q8C2×C22⋊D1314yes—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4C2×C22⋊D1312yes—
220C22×C4C2×C22⋊D1311yescharacteristic
221Q16—528no—
222M16—522no—
223C2×C8—262no—
224C2×C8—264no—
225C4⋊C4—216no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4—24no—
230C4⋊C4—24no—
231C4⋊C4—262no—
232C4⋊C4—262no—
233C4⋊C4—522no—
234C4⋊C4C2×C22⋊D1314yes—
235C22⋊C4—521no—
236C42—28no—
237C42—24no—
238C42—24no—
239C42—521no—
240C42C2×C22⋊D1311yescharacteristic
241C42C2×C22⋊D1312yes—
242C42C23×D1311yescharacteristic
243C13#1855111yescharacteristic, complemented, Sylow
244C23#8820711yescharacteristic
245Q8—28no—
246Q8—24no—
247Q8—44no—
248Q8—82no—
249Q8—88no—
250Q8—524no—
251Q8#8819618yes—
252C2×C4—28no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—522no—
261C2×C4#8820712yes—
262C2×C4#8820711yescharacteristic
263C2×C4C22×C22⋊D1311yescharacteristic
264C2×C4C22×C22⋊D1312yes—
265C8—522no—
266C8—524no—
267C22—22no—
268C22#1171890312yes—
269C22C2×#8820711yescharacteristic
270C4—21no—
271C4—21no—
272C4—28no—
273C4—22no—
274C4—44no—
275C4—44no—
276C4—1042no—
277C4C2×#8819614yes—
278C2—22no—
279C2#1312407012yes—
280C2C2×#1171890311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×Q82×C13C2
socleC22×C13C2×#120
prime radicalC23×C13#120
hypercenterC2×Q82D13
hypocenterC13#18551
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×Q82

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13114057C2semidirect
243. C13#18551semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131252162
#131249662
#131140572
#131135622
#131132832
C2×Q82×C132
#1855113